14 - 2 Observability S. Lall, Stanford 2009.11.09.01 The Key Points of This Section • once we know u (0) , . . . , u ( T − 1) and y (0) , . . . , y ( T − 1) , we just have a linear equation relating the data to the initial state x (0) • so we can use least squares to estimate it • and we can compute the estimation ellipsoid • which tells how sensitive the estimate is to errors • the infnite-time case is easy to compute via a Lyapunov equation • which gives a practical measure oF observability